Summary: This study considers a general production and delivery integration problem, commonly faced by a manufacturer that adopts make-to-order and commit-to-delivery business strategies. In the problem, the manufacturer determines acceptance or rejection of customers, produces products for accepted customers, and cooperates with third-party logistics providers who offer multiple shipping modes chosen by the manufacturer to deliver the finished products to customers. To better reflect the practical needs, this problem takes into account nonlinear production cost functions, nonlinear earliness and tardiness penalty functions, and nonlinear shipping cost functions of both shipping time and shipping quantity. The problem is to determine an integrated customer acceptance, production, and delivery plan by minimizing the total cost of production, shipping and inventory holding, and the total penalty of rejection, earliness, and tardiness. We investigate two variants of the problem where splittable delivery for the orders from customers is allowed and where splittable delivery is not allowed. For both the variants, we develop exact algorithms which achieve pseudo-polynomial running time in some practical situations, and design column generation-based heuristic algorithms to find near-optimal solutions efficiently. The computational results demonstrate that the heuristic algorithms are capable of generating near-optimal solutions for the instances generated randomly, with average optimality gap less than 4% in a reasonable running time.